The theory of unitary group representations began with finite groups, and blossomed in the twentieth century both as a natural abstraction of classical harmonic analysis, and as a tool for understanding various physical phenomena. Combining basic theory and new results, this monograph is a fresh and self-contained exposition of group representations and harmonic analysis on solvable Lie groups. Covering a range of topics from stratification methods for linear solvable actions in a finite-dimensional vector space, to complete proofs of essential elements of Mackey theory and a unified development of the main features of the orbit method for solvable Lie groups, the authors provide both well-known and new examples, with a focus on those relevant to contemporary applications. Clear explanations of the basic theory make this an invaluable reference guide for graduate students as well as researchers.

‘There is … the included background material on Lie theory, and there are also quite a lot of examples provided. Aspiring researchers in this area will likely find these features helpful, both aspiring and current researchers should also appreciate the wealth of material found here, as well as the extensive (five page, 92 entries) bibliography.’

Mark Hunacek Source: MAA Reviews

‘… embeddings into matrix algebras and unitary representations are both possible and useful, and they are given a central role in this book.’

M. Bona Source: Choice

'Throughout the book, the authors carefully explain the theory step by step and provide many concrete examples with computations which help the readers to understand. This book is a valuable exposition and an excellent research guide for the basic representation theory of solvable Lie groups for graduate students and researchers.'

Junko Inoue Source: MathSciNet

‘This monograph is a summary of a long career and experience of two great experts in their domain. Clear explanations of the basic theory make this an invaluable reference guide for graduate students as well as researchers. The concrete and example-based exposition is accessible to advanced graduate students and non-specialists.'

Béchir Dali Source: zbMATH